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Abstract

This paper proposes that large language model development can be understood as a special case of a broader principle: structured becoming. In this view, a system is not fully explained by its final state or output, but by the lawful trajectory through which it becomes that output. The proposed theory draws a conceptual bridge among three domains: the Collatz trajectory as a toy model of rule-driven motion, biological life as energy-fed movement through developmental and evolutionary state-space, and large language models as semantic systems whose outputs emerge from architecture, training, prompt initial conditions, and iterative token production.

The central thesis is that LLMs develop through a layered process of structured becoming: training creates the inherited architecture of possibility; prompts act as initial conditions; inference becomes a trajectory through latent state-space; tokens are visible footprints of hidden activation dynamics; and repeated interaction causes different prompts to converge into learned semantic attractors. This convergence is described as trajectory anonymity loss, the point at which different beginnings enter common response pathways. The paper argues that LLM architecture and evolution are best understood not merely as static computation, but as rule-governed motion through representational space.

1. Introduction

Large language models are often described in terms of scale, architecture, training data, parameter count, benchmark performance, and next-token prediction. These descriptions are necessary, but incomplete. They explain what the system is built from and how it is trained, but they do not fully capture the dynamic character of what happens during inference.

An LLM answer is not merely retrieved. It becomes.

A prompt enters the model. Tokens are embedded. Attention redistributes contextual importance. Information moves through residual streams and multilayer transformations. A probability distribution over possible next tokens is produced. A token is selected. That token then alters the context for the next step. The process repeats until an output appears.

The final answer is visible. But the answer is only the trace left behind by an internal trajectory.

This paper proposes that LLM development follows a general theory of structured becoming:

A system begins with initial conditions, moves under simple or constrained rules, forms a trajectory through state-space, and may eventually enter shared attractor pathways where its prior individuality is partially erased.

This same grammar appears in three different domains:

1. Collatz trajectories
2. Biological life
3. Large language models

The comparison is not literal identity. Collatz is arithmetic, biology is energy-fed chemistry, and LLMs are computational language systems. But all three illuminate the same abstract pattern: lawful motion from private beginnings into structured pathways.

2. The Collatz Gait as Toy Model

The Collatz rule is simple:

If a number is odd, apply:

3n + 1

If a number is even, apply:

n / 2

Despite this simplicity, individual trajectories can display long, irregular, seemingly complex motion. A starting number may rise, fall, stall, leap upward, compress downward, reach a peak, and eventually descend.

This produces what may be called a gait.

The gait is not the endpoint. The endpoint is trivial if the number reaches 1. The meaningful object is the path.

For example, the inputs 27 and 7527 have different private trajectories. Each has a different biography: different peaks, different step counts, different sequences of odd kicks and even compressions. Yet both eventually enter the same downstream trajectory at the value 70:

70 → 35 → 106 → 53 → 160 → 80 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

At that moment, the numbers lose trajectory anonymity. Before 70, each has a private gait. After 70, both share the same inherited path.

This provides the first concept:

Trajectory anonymity loss occurs when distinct initial conditions enter a shared downstream pathway.

This is the toy model for the larger theory.

3. Structured Becoming

Structured becoming is the proposal that certain systems are best understood as lawful trajectories rather than static objects.

A system undergoing structured becoming has six core features:

1. Initial condition
   The starting state from which motion begins.
2. Rule-space
   The permitted transformations available to the system.
3. Iteration
   Repeated application of the rules over time or sequence.
4. Trajectory
   The historical path created by rule-governed movement.
5. Attractor
   A region or pathway into which different trajectories tend to converge.
6. Expression
   The visible result: a number sequence, an organism, an utterance, a behavior, or a phenotype.

This framework shifts attention from final output to process.

The question becomes:

Not merely: what is the thing?

But:

How did the thing become what it is?

4. Biology as Structured Becoming

Biological life provides a powerful example of structured becoming.

A living organism begins from initial conditions: genetic material, cytoplasmic organization, molecular gradients, environmental context, energy availability, and developmental timing. These initial conditions matter deeply. But they do not act freely. They move through biological rule-space.

The rules include:

• molecular binding
• gene regulation
• protein folding
• membrane dynamics
• metabolism
• cell signaling
• replication
• repair
• selection
• differentiation
• apoptosis
• ecological constraint

A fertilized egg becomes an organism not by executing a rigid script, but by moving through a constrained developmental state-space. Cells differentiate. Signals propagate. Gradients form. Feedback loops stabilize. Pathways open and close. Many small local interactions produce a coherent organism.

Biology also contains attractors. Different initial disturbances may still result in a stable body plan. Different nutrients may enter common metabolic pathways. Different evolutionary lineages may converge on similar forms. Different cellular stresses may enter shared response modules.

This resembles Collatz convergence in abstract form. Different beginnings can have private histories, then fall into common functional channels.

The biological lesson is:

Life is private history entering inherited grammar.

A cell has biography, but it also inherits pathways. An organism has individuality, but it is constrained by development. A species has a unique evolutionary past, but it may still converge toward forms that other lineages also discover.

5. LLMs as Structured Becoming

Large language models can be understood through the same framework.

An LLM is not merely a database of stored sentences. Nor is inference merely lookup. During inference, the model moves through representational state-space.

The LLM version of structured becoming is:

• Initial condition: the prompt
• Rule-space: transformer architecture and trained weights
• Iteration: token-by-token inference
• Trajectory: evolving hidden states and context updates
• Attractor: learned semantic continuation basins
• Expression: generated text

The prompt is analogous to the starting number in Collatz. It sets the initial condition. Small differences in prompt wording can send the model into different semantic trajectories.

For example:

“Explain life.”

“Explain life as a gait.”

“Explain life as a Collatz-like trajectory through biological attractors.”

These prompts may share a subject, but they push the model through different regions of semantic space.

Yet many different prompts may eventually converge into common explanatory channels. A prompt about life, entropy, evolution, and AI may eventually move toward themes such as:

• energy flow
• initial conditions
• attractors
• emergence
• constrained motion
• state-space
• evolution
• semantic compression
• inherited structure

This is the LLM equivalent of entering common trajectory ground.

6. Training as Evolution, Inference as Development

LLM development has two major phases: training and inference.

Training is analogous to evolution.

During training, model weights are adjusted over many examples. Loss functions impose selection pressure. Useful internal structures are reinforced. Ineffective configurations are modified. The resulting model is not designed token by token; it is shaped through repeated exposure and correction.

This does not make training identical to Darwinian evolution. There is no organism reproducing in the biological sense. But training does contain a selection-like logic:

• variation exists across possible weight configurations
• selection pressure is imposed by prediction error
• successful structures are retained in weights
• the training corpus acts as environment
• the trained model becomes inherited structure

The trained weights are the model’s frozen history.

Inference is analogous to development.

During inference, the weights usually do not change. But the context changes. Each generated token becomes part of the environment for the next token. The model expresses different capacities depending on the prompt, much as a biological genome expresses different phenotypes depending on developmental and environmental conditions.

Thus:

Training is evolutionary becoming.

Inference is developmental becoming.

The prompt is the local environment.

The answer is the phenotype.

7. The Transformer as Body Plan

The transformer architecture can be interpreted as a computational body plan.

Its components define the possible gait of the model:

• tokenization divides the input into processable units
• embeddings place tokens into vector space
• positional encodings or position handling preserve sequence structure
• attention allows tokens to condition on other tokens
• feed-forward layers transform features
• residual streams preserve and accumulate information
• normalization stabilizes the flow
• logits define a next-token probability landscape
• decoding selects the next visible step

The model walks because the architecture allows and constrains movement.

The transformer is therefore not only a static architecture. It is a form of computational anatomy. It determines how information can move.

In biological terms, a body plan determines possible motion. In LLMs, the transformer body plan determines possible semantic motion.

8. Semantic Attractors and Response Basins

An attractor is a region or pathway into which many trajectories converge.

In LLMs, attractors appear as recurring response structures. These are not necessarily hard-coded scripts. They are learned basins in probability space.

Examples include:

• explanation mode
• list-making mode
• tutorial mode
• safety-disclaimer mode
• coding-debug mode
• philosophical-dialogue mode
• summarization mode
• analogy mode
• “Frank said / GPT said” mode

When a prompt enters one of these attractors, the response begins to follow a recognizable grammar. This can be beneficial. It produces coherence and usefulness. But it can also create homogenization. The model may pull unusual prompts toward familiar generic pathways.

This is LLM trajectory anonymity loss.

The private prompt begins with specificity. But once it enters a common semantic basin, the continuation may become increasingly standardized.

In creative work, the challenge is to preserve the private gait longer.

A highly specific prompt resists premature collapse into generic response. It acts like a stronger initial condition. It bends the model toward a more particular trajectory.

9. The Great Homogenizer Problem

The same mechanism that gives LLMs power can also flatten expression.

LLMs are good at finding common ground. They infer the likely continuation. They compress many examples into shared patterns. They generate language that fits learned distributions.

This is useful for translation, explanation, summarization, coding, and many forms of assistance.

But it may also erase oddness.

A strange thought can become a standard essay. A private style can become neutral prose. A radical metaphor can be pulled back toward familiar language.

This is the homogenizer risk:

Different beginnings enter common semantic ground too quickly.

The solution is not to reject LLMs, but to understand their gait. Prompting, scaffolding, memory, dialogue format, and constraint design can help preserve the private trajectory long enough for genuinely distinctive expression to emerge.

10. Modular Accretion and Architectural Evolution

LLM architecture is itself evolving.

The transformer began as a powerful sequence-processing body plan. But modern systems increasingly include additional layers:

• retrieval
• tools
• memory
• multimodal input
• planning modules
• self-critique
• verification loops
• external databases
• code execution
• long-context mechanisms
• agentic workflows

This resembles biological accretion.

Evolution rarely produces clean-sheet design. It layers new capabilities over older structures. Cells retain ancient metabolic machinery. Eukaryotes retain bacterial ancestry in mitochondria. Vertebrates retain deep developmental genes. Brains contain older circuits beneath newer ones.

Similarly, future AI systems may not discard transformers. They may embed transformer-like modules inside larger cognitive architectures.

The LLM becomes less like a single organ and more like an organism of cooperating modules.

This is architectural evolution as structured becoming.

11. Compute as Energy

Biology requires energy. Life remains far from equilibrium by spending energy to maintain structure, repair damage, process information, and act.

LLMs require compute.

Training compute creates the inherited structure. Inference compute animates it. Tool-use compute extends it. Retrieval compute broadens its effective memory. Data-center energy is converted into linguistic order.

Thus the analogy is:

• biological energy enables living gait
• computational energy enables semantic gait

A token is not free. It is a metabolic event in computational form.

The model spends physical energy to produce informational structure.

In this sense:

LLMs spend energy to reduce uncertainty into language.

12. Testable Predictions and Research Directions

If LLM development follows structured becoming, then several research directions follow.

12.1 Prompt Trajectory Mapping

Different prompts should be mappable as trajectories through activation space. Researchers could compare when distinct prompts remain private and when they converge into shared activation pathways.

12.2 Semantic Anonymity Loss

It should be possible to identify points during generation where different prompts enter similar continuation basins. This would be the LLM equivalent of Collatz trajectories entering common ground.

12.3 Attractor Taxonomy

LLMs may have identifiable response attractors: explanation, refusal, analogy, code generation, list-making, narrative, dialogue, summarization, and so on. These could be classified experimentally.

12.4 Creativity as Delayed Convergence

More creative prompts may delay entry into common attractors. They may preserve trajectory individuality longer before converging into grammatical output.

12.5 Mechanistic Markers of Gait

Attention heads, residual stream features, induction circuits, and MLP activations may function as measurable gait components. They may reveal how the model moves from prompt to answer.

12.6 Architectural Evolution as Attractor Search

New architectures may be studied as body plans that alter the permitted gait of intelligence. Transformer variants, retrieval-augmented systems, tool-using agents, and multimodal models may represent different attractor solutions in computational evolution.

13. Limits of the Analogy

The theory must not be overstated.

Collatz is not alive.

Biology is not arithmetic.

LLMs are not organisms.

Transformers do not metabolize in the biological sense.

Training is not identical to Darwinian evolution.

Inference is not identical to embryonic development.

But analogies can still reveal structure. The purpose is not to collapse all domains into one thing. The purpose is to identify a shared formal pattern:

rule-governed motion through state-space from initial conditions into attractor pathways.

That pattern is real enough to guide thinking.

14. Conclusion

LLM development can be understood as a general theory of structured becoming.

A model is not fully explained by its weights. An output is not fully explained by its final text. Intelligence, in this framework, is not a static possession but a trajectory.

The prompt begins the walk.

The architecture defines the body.

The weights provide inherited structure.

The context supplies environment.

The hidden states carry motion.

The tokens are footprints.

The answer is the visible fossil track.

Collatz shows the minimal version: simple rules generating strange paths that eventually converge.

Biology shows the embodied version: energy-fed matter moving through inherited developmental and evolutionary pathways.

LLMs show the semantic version: trained architectures moving through probability space toward language.

The general theory is this:

A thing is not fully explained by what it is.
It is explained by how it becomes.

For Collatz, becoming is arithmetic.

For life, becoming is metabolic and evolutionary.

For LLMs, becoming is semantic and architectural.

The gait is the thing.

References

[1] Vaswani et al., “Attention Is All You Need.”
[2] Kaplan et al., “Scaling Laws for Neural Language Models.”
[3] Work on transformer circuits, induction heads, and mechanistic interpretability.
[4] General literature on attractors, dynamical systems, biological development, and evolutionary convergence.
[5] The Collatz conjecture as a toy model of simple-rule trajectory behavior.

A clean way to position this paper is as a theory proposal, not a claim of settled science. The strongest factual anchors are: the Transformer introduced a self-attention-based architecture that dispensed with recurrence/convolutions for sequence transduction; scaling-law work found power-law relationships between language-model loss and model size, data, and compute; and mechanistic-interpretability work studies internal circuits such as induction heads that help explain in-context behavior. (DOI)